Quadratic approximation of solutions for boundary value problems with nonlocal boundary conditions

Authors:
Li Sun;Mingru Zhou;Guangwa Wang
Affiliations:
School of Mechanics and Civil Engineering, China University of Mining & Technology, Xuzhou 221008, PR China and School of Mathematics, Xuzhou Normal University, Xuzhou 221116, PR China;School of Mathematics, Xuzhou Normal University, Xuzhou 221116, PR China;School of Mathematics, Xuzhou Normal University, Xuzhou 221116, PR China
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, using the quasilinearization method coupled with the method of upper and lower solutions, we study a class of second-order nonlinear boundary value problems with nonlocal boundary conditions. We establish some sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem. An example is also included to illustrate the main result.